Non-credible threat

A threat, and its counterpart – a commitment, are both defined by American economist and Nobel prize winner, T.C.

[1] A non-credible threat is made on the hope that it will be believed, and therefore the threatening undesirable action will not need to be carried out.

[1] Eric van Damme's Extensive Form Game demonstrates another example of a non-credible threat.

[6] Therefore, in real world applications, the assumption that all players will be rational and act to maximise their utility is not practical, thus non-credible threats cannot be ignored.

[7] Nicolas Jacquemet and Adam Zylbersztejn conducted experiments based on the Beard and Beil Game to investigate whether people act to maximise their payoffs.

[8] In real world applications, non-credible threats must be considered as there is a high possibility players will not act rationally.

Illustration that shows the difference between a SPNE and another NE. The blue equilibrium is not subgame perfect because player two makes a non-credible threat at 2(2) to be unkind (U).
Player 2 threatening action A if Player 1 chooses action B is a non-credible threat. This is because if Player 1 chooses action B, Player 2 will choose action B, as this results in a higher payoff than action A for Player 2.